Paulsen and Projection Problems for Banach Spaces

TL;DR

This paper extends the classical Paulsen and projection problems from Hilbert spaces to Banach spaces, exploring their formulations and potential solutions in this broader context.

Contribution

It introduces formulations of the Paulsen and projection problems specifically for Banach spaces, building on prior work in Hilbert spaces.

Findings

Formulated the Paulsen problem for Banach spaces.

Formulated the projection problem for Banach spaces.

Established foundational concepts for further research.

Abstract

Based on the two decades old celebrated Paulsen problem and its solutions for Hilbert spaces by Kwok, Lau, Lee, Ramachandran, Hamilton, and Moitra, we formulate Paulsen problem for Banach spaces. We also formulate projection problem for Banach spaces.